2006 USAMO Problems/Problem 6

Problem

Let $\displaystyle ABCD$ be a quadrilateral, and let $\displaystyle E$ and $\displaystyle F$ be points on sides $\displaystyle AD$ and $\displaystyle BC$ , respectively, such that $\displaystyle AE/ED = BF/FC$ . Ray $\displaystyle FE$ meets rays $\displaystyle BA$ and $\displaystyle CD$ at $\displaystyle S$ and $\displaystyle T$ respectively. Prove that the circumcircles of triangles $\displaystyle SAE, SBF, TCF,$ and $\displaystyle TDE$ pass through a common point.

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2006 USAMO Problems/Problem 6

Problem

Solution

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